Find the number of units that produces maximum profit

Question

Find the number of units, x, that produces the maximum profit P, if C(x) = 250 + 52x and p = 72 - 2x

Answer 1

Hello Joseph,

Profit = Revenue - Cost

We need to find an equation for the revenue R(x).

R(x) = number of units * unit price = x * p(x) = x(72-x) = 72x - x²

Therefore: Profit P(x) = 72x - x² - (250 + 52x) = - x² + 20x -250

To find max profit, run the 1st derivative test, so set P'(x) = 0 and solve for x:

P'(x) = -2x + 20

set P'(x) = 0 ----> -2x+20 = 0 ----> -2x = -20 -----> x = 10

The number of units, x, that produces the maximum profit is 10.

Cheers.